A homeless suspect charged with killing a stranger by pushing him into the path of a New York City subway train told investigators his victim “rolled like a bowling ball” after he landed on the tracks, according to court papers.

In written and videotaped statements, Naeem Davis admitted watching as Ki-Suck Han tried in vain to climb off the tracks before the train hit him, the document prepared by prosecutors says.

Davis, 30, described Han as a drunken instigator of the deadly altercation on a subway platform near Times Square. But he also wrote that he was to blame and “shouldn’t have let this happen,” the document says.

The papers were made public on Tuesday as Davis pleaded not guilty to murder and manslaughter charges at a Manhattan courthouse. He’s been held without bail since his arrest last month.

Davis “had not been bothering anybody” when Han “went after him,” defense attorney Stephen Porkart told reporters outside court. If there was a push, it occurred out of frustration, he added.

Han’s wife has said she had argued with her husband and that he had been drinking on the morning of Dec. 3. At about 12:30 p.m., Han encountered Davis, who later told police he was on a paid errand to buy merchandise for street vendors.

Davis claimed that after the men accidentally bumped into each other while entering the station, the 58-year-old Han began yelling, “I’ll kill you!” He also said Han was staggering and slurring his words.

After Han followed Davis down the platform and tried to grab him, Davis admitted pushing him away. He described Han falling “head first onto the tracks and rolling like a bowling ball,” the document says.

At least a minute passed before the train hit the victim. Then Davis said he “freaked” and made his escape.

Davis claimed he didn’t intend to kill Han and was only defending himself, the document adds.

The defendant told investigators that he came to the United States from Sierra Leone in 1989, and that he once attended college in Pennsylvania.